Recursive Function Definition over Coinductive Types

• Authors: John Matthews
• Venue: TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
• Year: 1999

Using the notions of unique fixed point, converging equivalence relation, and contracting function, we generalize the technique of well-founded recursion. We are able to define functions in the Isabelle theorem prover that recursively call themselves an infinite number of times. In particular, we can easily define recursive functions that operate over coinductively-defined types, such as infinite lists. Previously in Isabelle such functions could only be defined corecursively, or had to operate over types containing "extra" bottom-elements. We conclude the paper by showing that the functions for filtering and flattening infinite lists have simple recursive definitions.